Séminaire de Mathématique

Symmetries of crystallographic groups

by Prof. Andrzej SZCZEPANSKI (University of Gdansk & IHES)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

Let G be a crystallographic group of dimension n, i.e. a discrete, cocompact subgroup of Isom(R^n) = O(n) \ltimes R^n. By symmetries of G we understand a group Out(G). For any n ≥ 2, we shall construct a crystallographic group with trivial center and a trivial outer automorphism group. Moreover, we shall present properties of an example (constructed by R. Waldmuler in 2003) of the torsion free crystallographic group of dimension 141 with a trivial center and a trivial outer automorphism group. (It is a joint work with R. Lutowski.)

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